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Benha University Time : 3 Hrs

Benha High Institute of Technology Department : Electrical Engineering

Jan 2011 – Fall semester Course name : E211 Digital Logic Circuit

Exam (Regular), Year : 2^nd

Time Allowed: Hours
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Attempt all questions

Q1) (12 points)

If the state of a 12 bit register is 1010 1101 1100. What is its content if it represents

(1)-Three decimal digits in BCD (2)- Three decimal digits in excess-3 code.

(3)-Three decimal digits in 84-2-1 (4)- A decimal number

*Answer*

XXX
7X9
6XX
2780 whereX is invalid Code For Decimal Digits

List the numbers from 10 to 26 in base 12.

*Answer*

A, B, 10,11,12,13,,14,15,`16,17,18,19,1A,1B,20,21,22

Assume a 3- input AND gate with output F and a 3- input OR gate with output G. The inputs are A, B, and C. show the signals by means of timing diagram of the outputs F and G as function of the 3 inputs ABC (use all 8 possible ABC combinations).

A
B
C

G
Q2) (12 points)

List the truth table of the function
*Answer*

F= xy + xy^\ + y^\z =Σ(1,4,5,6,7)

X	Y	Z	F
0	0	0	0
0	0	1	1
0	1	0	0
0	1	1	0
1	0	0	1
1	0	1	1
1	1	0	1
1	1	1	1
	1
1	1	1	1

Express the Complement of the following functions in sum of minterms.

F1(A,B,C,D) = Σ(0,2,6,11,13,14) , F2(x,y,z)= П(0,3,6,7)

*Answer*

F1^\ = Σ(1,3,4,5,7,8,9,10,12,15) F2^\ = Σ( 0,3,6,7)

show that the dual of a Two input XOR is equal to its complement

*Answer*

XOR= XY^\+ X^\Y

Complement = (XY\ + X\Y)\= (XY\)\ (X\Y)\ = (X\ +Y)( X + Y\)= X\ X + Y Y\ + xy + x\y\= xy+x\y\=XNOR------ 1

Dual = (x+y\)(x\+y)=xx\+xy+x\y\+yy\=xy+x\y\=XNOR----------2

1=2
Q3) (12 points)

For the function F (A,B,C,D) = Σ (0,1,2,3,4,8,9,12)

Simplify the function with the suitable map.
Implement the function with two level AND- OR gates
Implement the function with two level NAND gates.
Implement the function with two level NOR- OR.

1	1	1	1
1	0	0	0
1	0	0	0
1	1	0	0

*Answer*
F= A\B\ + C\D\ + B\C\

Q4) (16 points)

For circuit that operate as a Full Adder, construct a truth table, simplify the function obtained by the truth table, and implement the simplified function with suitable gates.

*Answer*

X	Y	Z	S	C
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

Repeat the above item for code conversion circuit that converts from BCD code into excess-3 code, taking the unused combinations as Don’t Care conditions.

Q5) (8 points)

Analyze the given circuit below to obtain the logic function for F1 & F2.

*Answer*

F1= T2 + T3

T1 = (A+B +C)\ = A\B\C\

T2 = ABC
F2 = AB + AC + (BC)\ = AB + AC + B\ + C\ ------------------------1
F2\ = (AB)\(AC)\(BC)
T3 = T1.F2\ = (A\B\C\)(AB)\(AC)\(BC)
F1 = T2 + T3 = ABC + (A\B\C\)(AB)\(AC)\(BC)--------------------2

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